[ 4 0] [-2 -3] What is the Adj of this matrix
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the elements of the matrix.
The given matrix is:
$$A = \begin{bmatrix} 4 & 0 \\ -2 & -3 \end{bmatrix}$$
Here, $a=4$, $b=0$, $c=-2$, and $d=-3$.
Step 2: Apply the formula for the adjoint of a $2 \times 2$ matrix.
For a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, the adjoint matrix is given by:
$$\text{Adj}(A) = \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$$
Step 3: Substitute the values from the given matrix into the adjoint formula.
$$\text{Adj}(A) = \begin{bmatrix} -3 & -(0) \\ -(-2) & 4 \end{bmatrix}$$
Step 4: Simplify the elements.
$$\text{Adj}(A) = \begin{bmatrix} -3 & 0 \\ 2 & 4 \end{bmatrix}$$
The adjoint of the matrix is $\boxed{\begin{bmatrix} -3 & 0 \\ 2 & 4 \end{bmatrix}}$.
